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|00000000| 5c 63 68 61 70 74 65 72 | 7b 53 63 61 6c 61 72 73 |\chapter|{Scalars|
|00000010| 7d 0d 5c 69 6e 64 65 78 | 7b 73 63 61 6c 61 72 7c |}.\index|{scalar||
|00000020| 28 7d 0d 5c 73 65 63 74 | 69 6f 6e 7b 43 72 65 61 |(}.\sect|ion{Crea|
|00000030| 74 69 6e 67 20 53 63 61 | 6c 61 72 73 7d 0d 0d 5c |ting Sca|lars}..\|
|00000040| 73 65 63 74 69 6f 6e 7b | 53 63 61 6c 61 72 20 4f |section{|Scalar O|
|00000050| 70 65 72 61 74 69 6f 6e | 73 7d 0d 0d 5c 52 4c 61 |peration|s}..\RLa|
|00000060| 42 5c 20 68 61 73 20 61 | 20 77 69 64 65 20 72 61 |B\ has a| wide ra|
|00000070| 6e 67 65 20 6f 66 20 6f | 70 65 72 61 74 6f 72 73 |nge of o|perators|
|00000080| 20 74 6f 20 61 63 74 20 | 75 70 6f 6e 20 73 63 61 | to act |upon sca|
|00000090| 6c 61 72 73 2e 20 20 54 | 68 65 20 75 6e 61 72 79 |lars.  T|he unary|
|000000a0| 0d 6f 70 65 72 61 74 6f | 72 73 20 64 65 66 69 6e |.operato|rs defin|
|000000b0| 65 64 20 6f 6e 20 73 63 | 61 6c 61 72 73 20 61 72 |ed on sc|alars ar|
|000000c0| 65 3a 0d 0d 20 20 20 5c | 62 65 67 69 6e 7b 64 65 |e:..   \|begin{de|
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|000000e0| 20 20 20 5c 69 74 65 6d | 5b 2d 2d 5d 20 55 6e 61 |   \item|[--] Una|
|000000f0| 72 79 20 6e 65 67 61 74 | 69 6f 6e 20 69 73 20 74 |ry negat|ion is t|
|00000100| 68 65 20 68 69 67 68 65 | 73 74 20 70 72 69 6f 72 |he highe|st prior|
|00000110| 69 74 79 20 6f 70 65 72 | 61 74 6f 72 2e 20 0d 20 |ity oper|ator. . |
|00000120| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 49 |        |       I|
|00000130| 74 20 69 73 20 74 68 65 | 20 73 61 6d 65 20 61 73 |t is the| same as|
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|00000170| 20 20 20 72 69 67 68 74 | 20 6f 66 20 74 68 65 20 |   right| of the |
|00000180| 6f 70 65 72 61 74 6f 72 | 20 62 79 20 24 2d 31 24 |operator| by $-1$|
|00000190| 2e 0d 0d 20 20 20 20 20 | 20 20 20 5c 69 74 65 6d |...     |   \item|
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|000001c0| 70 65 72 61 74 65 73 20 | 6f 6e 20 74 68 65 20 6f |perates |on the o|
|000001d0| 70 65 72 61 6e 64 0d 20 | 20 20 20 20 20 20 20 20 |perand. |        |
|000001e0| 20 20 20 20 20 20 20 74 | 6f 20 74 68 65 20 6c 65 |       t|o the le|
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|00000200| 6f 72 2e 20 49 66 0d 20 | 20 20 20 20 20 20 20 20 |or. If. |        |
|00000210| 20 20 20 20 20 20 20 74 | 68 65 20 69 6d 61 67 69 |       t|he imagi|
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|00000230| 20 6f 70 65 72 61 6e 64 | 20 69 73 20 7a 65 72 6f | operand| is zero|
|00000240| 2c 20 6f 6e 6c 79 20 74 | 68 65 0d 20 20 20 20 20 |, only t|he.     |
|00000250| 20 20 20 20 20 20 20 20 | 20 20 20 72 65 61 6c 20 |        |   real |
|00000260| 70 61 72 74 20 69 73 20 | 69 6e 63 72 65 6d 65 6e |part is |incremen|
|00000270| 74 65 64 2c 20 6f 74 68 | 65 72 77 69 73 65 20 62 |ted, oth|erwise b|
|00000280| 6f 74 68 20 72 65 61 6c | 20 61 6e 64 0d 20 20 20 |oth real| and.   |
|00000290| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 69 6d 61 |        |     ima|
|000002a0| 67 69 6e 61 72 79 20 70 | 61 72 74 73 20 61 72 65 |ginary p|arts are|
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|000002d0| 2d 2d 5d 20 20 44 65 63 | 72 65 6d 65 6e 74 73 20 |--]  Dec|rements |
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|00000340| 20 20 20 20 20 20 74 68 | 65 20 69 6d 61 67 69 6e |      th|e imagin|
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|00000360| 6f 70 65 72 61 6e 64 20 | 69 73 20 7a 65 72 6f 2c |operand |is zero,|
|00000370| 20 6f 6e 6c 79 20 74 68 | 65 0d 20 20 20 20 20 20 | only th|e.      |
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|000003e0| 64 65 63 72 65 6d 65 6e | 74 65 64 2e 0d 0d 20 20 |decremen|ted...  |
|000003f0| 20 5c 65 6e 64 7b 64 65 | 73 63 72 69 70 74 69 6f | \end{de|scriptio|
|00000400| 6e 7d 0d 0d 4c 65 74 73 | 20 6c 6f 6f 6b 20 61 74 |n}..Lets| look at|
|00000410| 20 74 68 65 20 76 61 72 | 69 6f 75 73 20 62 69 6e | the var|ious bin|
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|00000430| 66 6f 72 20 5c 76 65 72 | 62 2b 41 20 62 69 6e 6f |for \ver|b+A bino|
|00000440| 70 20 42 2b 3a 0d 0d 20 | 20 20 5c 62 65 67 69 6e |p B+:.. |  \begin|
|00000450| 7b 64 65 73 63 72 69 70 | 74 69 6f 6e 7d 0d 20 20 |{descrip|tion}.  |
|00000460| 20 20 20 5c 69 74 65 6d | 5b 2b 5d 20 41 64 64 73 |   \item|[+] Adds|
|00000470| 20 74 68 65 20 6f 70 65 | 72 61 6e 64 73 2e 0d 0d | the ope|rands...|
|00000480| 20 20 20 20 20 5c 69 74 | 65 6d 5b 2d 2d 5d 20 53 |     \it|em[--] S|
|00000490| 75 62 74 72 61 63 74 73 | 20 74 68 65 20 73 65 63 |ubtracts| the sec|
|000004a0| 6f 6e 64 20 6f 70 65 72 | 61 6e 64 20 66 72 6f 6d |ond oper|and from|
|000004b0| 20 74 68 65 20 66 69 72 | 73 74 20 6f 70 65 72 61 | the fir|st opera|
|000004c0| 6e 64 2e 0d 0d 20 20 20 | 20 20 5c 69 74 65 6d 5b |nd...   |  \item[|
|000004d0| 2a 5d 20 4d 75 6c 74 69 | 70 6c 69 65 73 20 74 68 |*] Multi|plies th|
|000004e0| 65 20 6f 70 65 72 61 6e | 64 73 20 74 6f 67 65 74 |e operan|ds toget|
|000004f0| 68 65 72 2e 20 0d 0d 20 | 20 20 20 20 5c 69 74 65 |her. .. |    \ite|
|00000500| 6d 5b 2f 5d 20 44 69 76 | 69 64 65 73 20 74 68 65 |m[/] Div|ides the|
|00000510| 20 66 69 72 73 74 20 6f | 70 65 72 61 6e 64 20 62 | first o|perand b|
|00000520| 79 20 74 68 65 20 73 65 | 63 6f 6e 64 20 6f 70 65 |y the se|cond ope|
|00000530| 72 61 6e 64 2e 0d 0d 20 | 20 20 20 20 5c 69 74 65 |rand... |    \ite|
|00000540| 6d 5b 24 5c 73 65 74 6d | 69 6e 75 73 24 5d 20 44 |m[$\setm|inus$] D|
|00000550| 69 76 69 64 65 73 20 74 | 68 65 20 66 69 72 73 74 |ivides t|he first|
|00000560| 20 6f 70 65 72 61 6e 64 | 20 62 79 20 74 68 65 20 | operand| by the |
|00000570| 73 65 63 6f 6e 64 20 6f | 70 65 72 61 6e 64 2e 20 |second o|perand. |
|00000580| 54 68 69 73 0d 69 73 20 | 74 68 65 20 73 61 6d 65 |This.is |the same|
|00000590| 20 61 73 20 74 68 65 20 | 72 69 67 68 74 20 64 69 | as the |right di|
|000005a0| 76 69 73 69 6f 6e 20 6f | 70 65 72 61 74 6f 72 20 |vision o|perator |
|000005b0| 6f 6e 20 73 63 61 6c 61 | 72 73 20 2d 2d 2d 20 69 |on scala|rs --- i|
|000005c0| 74 20 64 69 66 66 65 72 | 73 20 6f 6e 6c 79 0d 6f |t differ|s only.o|
|000005d0| 6e 20 6d 61 74 72 69 63 | 65 73 2e 0d 0d 20 20 20 |n matric|es...   |
|000005e0| 20 20 5c 69 74 65 6d 5b | 2e 2f 5d 20 44 69 76 69 |  \item[|./] Divi|
|000005f0| 64 65 73 20 74 68 65 20 | 66 69 72 73 74 20 6f 70 |des the |first op|
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|00000620| 73 0d 69 73 20 74 68 65 | 20 73 61 6d 65 20 61 73 |s.is the| same as|
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|00000640| 69 6f 6e 20 6f 70 65 72 | 61 74 6f 72 20 6f 6e 20 |ion oper|ator on |
|00000650| 73 63 61 6c 61 72 73 20 | 2d 2d 2d 20 69 74 20 64 |scalars |--- it d|
|00000660| 69 66 66 65 72 73 20 6f | 6e 6c 79 0d 6f 6e 20 6d |iffers o|nly.on m|
|00000670| 61 74 72 69 63 65 73 2e | 0d 0d 20 20 20 20 20 5c |atrices.|..     \|
|00000680| 69 74 65 6d 5b 24 2e 5c | 73 65 74 6d 69 6e 75 73 |item[$.\|setminus|
|00000690| 24 5d 20 44 69 76 69 64 | 65 73 20 74 68 65 20 66 |$] Divid|es the f|
|000006a0| 69 72 73 74 20 6f 70 65 | 72 61 6e 64 20 62 79 20 |irst ope|rand by |
|000006b0| 74 68 65 20 73 65 63 6f | 6e 64 20 6f 70 65 72 61 |the seco|nd opera|
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|000006f0| 74 6f 72 20 6f 6e 20 73 | 63 61 6c 61 72 73 20 2d |tor on s|calars -|
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|00000730| 4d 75 6c 74 69 70 6c 69 | 65 73 20 74 68 65 20 6f |Multipli|es the o|
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|00000770| 2a 2b 20 6f 70 65 72 61 | 74 6f 72 20 6f 6e 20 73 |*+ opera|tor on s|
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|00000790| 66 66 65 72 73 20 6f 6e | 6c 79 20 6f 6e 20 6d 61 |ffers on|ly on ma|
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|000007f0| 0d 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 70 |.       |       p|
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|00000840| 20 74 6f 20 74 68 65 0d | 20 20 20 20 20 20 20 20 | to the.|        |
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|000008d0| 20 20 20 5c 65 6e 64 7b | 64 65 73 63 72 69 70 74 |   \end{|descript|
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|00000ce0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 0d 20 |        |      . |
|00000cf0| 20 20 20 20 20 20 20 52 | 4c 61 42 20 65 71 75 61 |       R|LaB equa|
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|00000df0| 20 20 5c 52 4c 61 42 5c | 20 6c 6f 67 69 63 61 6c |  \RLaB\| logical|
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